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Nonparametric instrumental variable estimation

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  • Daniel Wilhelm
  • Denis Chetverikov
  • Dongwoo Kim

Abstract

This paper introduces Stata commands [R] npivreg and [R] npivregcv, which implement nonparametric instrumental variable (NPIV) estimation methods without and with a cross-validated choice of tuning parameters, respectively. Both commands are able to impose monotonicity of the estimated function. The use of such a shape restriction may signicantly improve the performance of the NPIV estimator (Chetverikov and Wilhelm 2017). This is because the ill-posedness of the NPIV estimation problem leads to unconstrained estimators that suffer from particularly poor statistical properties such as very high variance. The constrained estimator that imposes the monotonicity, on the other hand, signicantly reduces variance by removing oscillations of the estimator that is nonmonotone.We provide a small Monte Carlo experiment to study the estimators' finite sample properties and an application to the estimation of gasoline demand functions.

Suggested Citation

  • Daniel Wilhelm & Denis Chetverikov & Dongwoo Kim, 2017. "Nonparametric instrumental variable estimation," CeMMAP working papers 47/17, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:47/17
    DOI: 10.1920/wp.cem.2017.4717
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    References listed on IDEAS

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    1. Chetverikov, Denis & Wilhelm, Daniel & Kim, Dongwoo, 2021. "An Adaptive Test Of Stochastic Monotonicity," Econometric Theory, Cambridge University Press, vol. 37(3), pages 495-536, June.
    2. Denis Chetverikov & Dongwoo Kim & Daniel Wilhelm, 2018. "Nonparametric instrumental-variable estimation," Stata Journal, StataCorp LP, vol. 18(4), pages 937-950, December.
    3. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    4. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2012. "Measuring the price responsiveness of gasoline demand: Economic shape restrictions and nonparametric demand estimation," Quantitative Economics, Econometric Society, vol. 3(1), pages 29-51, March.
    5. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    6. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    7. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Escanciano, Juan Carlos & Li, Wei, 2021. "Optimal Linear Instrumental Variables Approximations," Journal of Econometrics, Elsevier, vol. 221(1), pages 223-246.
    2. Manuel Arellano & Stéphane Bonhomme, 2023. "Recovering Latent Variables by Matching," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 693-706, January.
    3. Jad Beyhum & Elia Lapenta & Pascal Lavergne, 2023. "One-step smoothing splines instrumental regression," Papers 2307.14867, arXiv.org, revised Dec 2024.
    4. Denis Chetverikov & Dongwoo Kim & Daniel Wilhelm, 2018. "Nonparametric instrumental-variable estimation," Stata Journal, StataCorp LP, vol. 18(4), pages 937-950, December.
    5. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Sep 2021.
    6. Christoph Breunig & Xiaohong Chen, 2020. "Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models," Cowles Foundation Discussion Papers 2238R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    7. Daniel Wilhelm, 2018. "Testing for the presence of measurement error," CeMMAP working papers CWP45/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2023. "Constrained Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 91(2), pages 709-736, March.
    9. Giovanni Compiani, 2022. "Market counterfactuals and the specification of multiproduct demand: A nonparametric approach," Quantitative Economics, Econometric Society, vol. 13(2), pages 545-591, May.
    10. Chetverikov, Denis & Wilhelm, Daniel & Kim, Dongwoo, 2021. "An Adaptive Test Of Stochastic Monotonicity," Econometric Theory, Cambridge University Press, vol. 37(3), pages 495-536, June.
    11. Anupriya, & Graham, Daniel J. & Bansal, Prateek & Hörcher, Daniel & Anderson, Richard, 2023. "Optimal congestion control strategies for near-capacity urban metros: Informing intervention via fundamental diagrams," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    12. Beyhum, Jad & Lapenta, Elia & Lavergne, Pascal, 2023. "One-step nonparametric instrumental regression using smoothing splines," TSE Working Papers 23-1467, Toulouse School of Economics (TSE).
    13. Qingliang Fan & Zijian Guo & Ziwei Mei & Cun-Hui Zhang, 2023. "Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity," Papers 2310.08063, arXiv.org, revised Jun 2024.
    14. Yu Zhu, 2020. "Inference in nonparametric/semiparametric moment equality models with shape restrictions," Quantitative Economics, Econometric Society, vol. 11(2), pages 609-636, May.
    15. Pengzhou Wu & Kenji Fukumizu, 2021. "$\beta$-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap," Papers 2110.05225, arXiv.org.
    16. Christoph Breunig & Xiaohong Chen, 2020. "Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models," Papers 2006.09587, arXiv.org, revised Nov 2024.
    17. Nishanth Dikkala & Greg Lewis & Lester Mackey & Vasilis Syrgkanis, 2020. "Minimax Estimation of Conditional Moment Models," Papers 2006.07201, arXiv.org.
    18. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2018. "Rate Optimal Specification Test When the Number of Instruments is Large," KIER Working Papers 986, Kyoto University, Institute of Economic Research.
    19. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.
    20. Anupriya, & Bansal, Prateek & Graham, Daniel J., 2023. "Congestion in cities: Can road capacity expansions provide a solution?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 174(C).
    21. Young Jun Lee & Daniel Wilhelm, 2020. "Testing for the presence of measurement error in Stata," Stata Journal, StataCorp LP, vol. 20(2), pages 382-404, June.

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